Merseytravel had planned to prevent a repeat of the disruption caused by last month's stoppage by keeping one of the tunnels open for the expected second strike.
Cllr Mark Dowd, chairman of Merseytravel, said: "It is pleasing to hear that people are getting around the table to hopefully find a solution to this issue, which is in the interests of everyone in Merseyside.
"If there is no strike action then it will obviously be business as usual."
The decision to recommend suspension of the action follows informal discussions between the two sides over recent days.
The individual unions will now hold the necessary internal consultations.
The unions were protesting about the decision to scrap the so-called 85-year rule, which allows council workers whose years of service and age add up to 85, to retire on a full pension.
It follows a ruling by the Government that the arrangement breached European age discrimination legislation.
Southport-born TUC general secretary Brendan Barber welcomed talks and said he believed detailed negotiations would start "urgently".
He said: "I am very pleased that it has now been possible to agree with the local government employers a sensible framework for the detailed negotiations."
Local Government Association chairman Sir Sandy Bruce-Lockhart said the suspension of the planned strike action would come as a "relief" to both sides as well as the public.
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